Vertical equilibrium models for coupled flow and transport problems
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A better understanding of viscous fingering can help to increase the recovery of hydrocarbons. The need for modelling the impact of viscous fingering is great as it largely dictates the sweep quality of hydrocarbons in a porous medium. In this study we will investigate the effects of viscous fingering in a porous medium by incorporating an unstable flow caused by a dynamic viscosity and gravity. Our approach will be to consider the permeability as a diagonal tensor with the permeabilities scaled as an exponent of the width of a thin-strip, where the flow is present. This thesis provides a rigorous approach towards the derivation of a 1D model and the quality of upscaling is further illustrated through an extensive study of numerical results.